Chapter 8.5, Problem 53AYU

Tuning Fork The end of a tuning fork moves in simple harmonic motion described by the equation $d=a\sin \left(\omega t\right)$. If a tuning fork for the note $A$ above middle $C$ on an even-tempered scale ( ${\text{A}}_4$, the tone by which an orchestra tunes itself) has a frequency of 440 hertz (cycles per second), find $\omega$. If the maximum displacement of the end of the tuning fork is $0.01$ millimeter, determine the equation that describes the movement of the tuning fork.

Source: David Lapp. Physics of Music and Musical Instruments. Medford, M A:Tufts University, 2003